ABSTRACT
The dynamics of flexible polymers in dilute solutions is studied taking into account the hydrodynamic memory, as a consequence of fluid inertia. As distinct from the Rouse-Zimm (RZ) theory, the Boussinesq friction force acts on the monomers (beads) instead of the Stokes force, and the motion of the solvent is governed by the nonstationary Navier-Stokes equations. The obtained generalized RZ equation is solved approximately using the preaveraging of the Oseen tensor. It is shown that the time correlation functions describing the polymer motion essentially differ from those in the RZ model. The mean-square displacement (MSD) of the polymer coil is at short times approximately t(2) (instead of approximately t). At long times the MSD contains additional (to the Einstein term) contributions, the leading of which is approximately t. The relaxation of the internal normal modes of the polymer differs from the traditional exponential decay. It is displayed in the long-time tails of their correlation functions, the longest lived being approximately t(-3/2) in the Rouse limit and t(-5/2) in the Zimm case, when the hydrodynamic interaction is strong. It is discussed that the found peculiarities, in particular, an effectively slower diffusion of the polymer coil, should be observable in dynamic scattering experiments.
ABSTRACT
The collective excitations of the compressible diluted emulsion are studied. The diluted emulsion is consisted of molecules with intrinsic momentum. The motion equation for fluctuation fields of the velocity, density, intrinsic momentum and pressure were chosen here in the form of linearized Navier-Stokes equations with constant shear and volume viscosity, and diffusion coefficient of momentum, spontaneous stresses. For simplicity in the calculations, temperature fluctuations were not taken into account. We assume that the emulsion possesses constant surface tension. For hydrodynamic fields excited by spontaneous sources, continuity conditions on the surface tangents of the velocity and stress tensor components should be satisfied at the interface. The boundary conditions for the normal force components comprise the excess Laplace pressure and the random surface force determined by the difference of the radial values of the spontaneous volume stress densities. Because of the smallness of the surface displacements, all the boundary conditions should be applied on sphere. To construct the spectral densities of the thermal fields caused by random surface forces, we used the fluctuation-dissipate theorem. The spectral densities of the thermal amplitude fluctuations of the hydrodynamic currents are expressed in terms of susceptibilities. The spectrum of fluctuations contains all the collective excitations of the emulsion associated with fluctuating motions of the surface and with the properties of near-surface currents. Their analysis, based on strict inequalities between the drop's emulsion size, the penetration depth of a viscous wave, and the wavelength of sound, essentially depends on the order of magnitude of the boundary transitions.
ABSTRACT
The spectra of Rayleigh scattering of Mössbauer radiation (RSMR) and Mössbauer absorption by globular macromolecules are calculated. The dependence of the spectra parameters on hydration is modeled with the account for thermal low-frequency vibrations of the particles constituting the globule. Deformational motions of the macromolecule fragments leading to deviations from its equilibrium spherical shape are considered introducing collective dynamical variables governed by Langevin equations with random sources of external forces. The macromolecule is modeled by a double-layered sphere: a rigid (elastic) core is surrounded by a porous hydration shell filled with fluid. The dynamical properties of the bound water inside the shell are described by the Debye-Brinkman equations. The degree of hydration is introduced by means of a combination of the mass coefficients of the porous shell with fluid and the mass coefficients in the limiting cases when the flow inside the shell is "frozen" and in the case of free flow. The hydration-dependent Lamb-Mössbauer factor and the elastic fraction of the RSMR are calculated and compared with experimental data from the literature.
